According to Deadline, Star Trek 4 has been shelved. This was part of the article regarding SJ Clarkson directing the pilot of the Game of Thrones prequel.
Deadline’s statement:
Clarkson was recruited by HBO for GOT after she recently became available. Earlier this year, Clarkson was the first female director to be tapped to direct a Star Trek movie when she was hired to helm the fourth feature in the current series. That project has since been shelved.
This comes as no surprise as both Chris Pine and Chris Hemsworth walked away from the project, due to salary negotiations falling apart. Paramount Pictures tried convince Pine and Hemsworth to take pay cuts, due to the performance of ‘Star Trek Beyond,’ to no avail.
Pine was due to reprise his role as Captain Kirk, while Hemsworth was planned to reprise his role as Kirk’s father. The plot was supposed to be a time-traveling adventure. This concept proves impossible without the two of them on board.
However, Paramount has previously set Mark L. Smith to write a script for an R-rated Star Trek movie. This film came from an idea by Quentin Tarantino, that he and JJ Abrams are set to produce. The film will most likely get into production soon, as a natural pivot from the lack of Pine’s Star Trek. Will we ever see a Star Trek 4? Only time will tell.
Source: Deadline